math: add SQT inverse method.

src/lol/math/transform.h

@@ -460,6 +460,24 @@ static inline quat_t<T> operator /(quat_t<T> const &x, quat_t<T> const &y)
 template<typename T>
 extern quat_t<T> slerp(quat_t<T> const &qa, quat_t<T> const &qb, T f);
 
+/*
+ * SQTs only
+ */
+
+template<typename T>
+static inline sqt_t<T> inverse(sqt_t<T> const &tr)
+{
+    auto inv_s = T(1) / tr.s;
+    auto inv_q = re(tr.q);
+    return sqt_t<T>(inv_s, inv_q, inv_q * tr.t * -inv_s);
+}
+
+template<typename T>
+static inline sqt_t<T> operator /(sqt_t<T> const &x, sqt_t<T> const &y)
+{
+    return x * inverse(y);
+}
+
 #if !LOL_FEATURE_CXX11_CONSTEXPR
 #undef constexpr
 #endif

src/t/math/sqt.cpp

@@ -72,6 +72,19 @@ lolunit_declare_fixture(sqt_test)
         }
     }
 
+    lolunit_declare_test(sqt_inverse)
+    {
+        for (vec4 v0 : test_vec4s)
+        {
+            vec4 v1 = inverse(test_sqt_1) * (test_sqt_1 * v0);
+
+            lolunit_assert_doubles_equal(v0.x, v1.x, 1e-5f);
+            lolunit_assert_doubles_equal(v0.y, v1.y, 1e-5f);
+            lolunit_assert_doubles_equal(v0.z, v1.z, 1e-5f);
+            lolunit_assert_doubles_equal(v0.w, v1.w, 1e-5f);
+        }
+    }
+
     lolunit_declare_test(sqt_composition_vec4)
     {
         /* We check that transforming a vec4 with an SQT and a